English

The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems

Logic in Computer Science 2015-07-01 v2 Logic

Abstract

We investigate wether three statements in analysis, that can be proved classically, are realizable in the realizability model of extensional continuous functionals induced by Kleene's second model K2K_2. We prove that a formulation of the Riemann Permutation Theorem as well as the statement that all partially Cauchy sequences are Cauchy cannot be realized in this model, while the statement that the product of two anti-Specker spaces is anti-Specker can be realized.

Cite

@article{arxiv.1502.02388,
  title  = {The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems},
  author = {Dag Normann},
  journal= {arXiv preprint arXiv:1502.02388},
  year   = {2015}
}
R2 v1 2026-06-22T08:25:12.811Z